Suppose that F ,G AND Q , and are polynomials and F( x)  / Q ( x) = G ( x )/Q (x  ) for all x  except when  Q ( x) =0 Prove that F( x)  = G ( x )  forall  x .

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter8: Polynomials
Section8.3: Factorization In F [x]
Problem 17E: Suppose that f(x),g(x), and h(x) are polynomials over the field F, each of which has positive...
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Suppose that F ,G AND Q , and are polynomials and

F( x)  / Q ( x) = G ( x )/Q (x  ) for all x  except when  Q ( x) =0 Prove that F( x)  = G ( x )  for
all  x . 

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